1. Field of the Invention
The present invention relates to an image forming apparatus which corrects so-called color misregistration, which is offset among multiple toner images provided on an image bearing member, by detecting a mark on the image bearing member using multiple sensors provided away from one another in the direction of movement of an image bearing belt.
2. Description of the Related Art
Japanese Patent Laid-Open No. 2005-156877 describes a technique wherein a mark provided on an intermediate transfer belt is detected by multiple sensors disposed at predetermined intervals in the direction of movement of the intermediate transfer belt (image bearing member). The speed of the intermediate transfer belt is calculated from the detection results of the sensors. The speed of the intermediate transfer belt changes according to change in the diameter of the driving rollers which rotate the intermediate transfer belt, leading to color misregistration. The image forming apparatus in Japanese Patent Laid-Open No. 2005-156877 corrects the color misregistration based on the speed calculated from the detection results of the sensors.
However, members supporting the above-mentioned sensors exhibit thermal expansion, due to the effects of change in temperature within the image forming apparatus. This thermal expansion causes change in the intervals between the sensors, leading to a state wherein precise detection cannot be performed and correction of color misregistration cannot be carried out in a precise manner.
The effects of thermal expansion of a supporting member which supports the sensors on the image will be described with an example of an image forming apparatus having multiple image forming units, wherein multiple toner images are overlaid on the intermediate transfer belt.
In a case wherein two sensors are supported at predetermined intervals by a sensor supporting member having a linear expansion coefficient of α, and the temperature change of the supporting member is ΔT, the sensor interval r between the sensors isr′=(1+α×ΔT)×r  (1)due to the linear expansion. Accordingly, the speed V of the intermediate transfer belt in an arrangement wherein the detection interval between the two sensors is tb can be expressed asV=(1+α×ΔT)×r/tb.  (2)
However, if we measure the speed of the intermediate transfer belt without taking into consideration this linear expression, as known arrangements do, the measured belt speed Ve isVe=r/tb.  (3)
The difference ΔV between the measured belt speed Ve and the true speed V of the belt is thus the error due to linear expansion of the supporting member.
                                                                        Δ                ⁢                                                                  ⁢                V                            =                              V                -                Ve                                                                                        =                              α                ×                Δ                ⁢                                                                  ⁢                T                ×                                  r                  /                  tb                                                                                        (        4        )            
Now, the positional offset amount ΔX on the intermediate transfer belt due to the speed error ΔV is as follows. Let us say that the interval between the two image forming units farthest from each other, out of the multiple image forming units, is an interval L. An image is formed by the first image forming unit of the apparatus onto the intermediate transfer belt, the intermediate transfer belt is transported by the distance L, and the apparatus is corrected such that, at precisely this time, the image formed by the second image forming unit which is at this distance is overlaid on the first image, and transferred.
Now, the target time ta to which the timing is to be set is the amount of time during which the intermediate transfer belt travels the distance L at the measured belt speed Ve, and accordinglyta=L/Ve  (5)holds. The positional offset occurring during this time ta due to the speed error ΔV thus is ΔX. Accordingly,ΔX=ΔV×ta  (6)holds, into which the Expressions (3), (4), and (5) are substituted, to yieldΔX=L×α×ΔT  (7)
For example, with an image forming apparatus wherein the supporting member of the two sensors is formed of iron which has a linear expansion coefficient of 11.7×10−6, and the interval between the four image forming units is 100 mm, temperature fluctuation of 5° C. at the sensor supporting member will result in color misregistration between the image forming units farthest from each other is as follows. That is to say, the interval L between the image forming units farthest from each other is 300 mm, so the amount of color misregistration therebetween is obtained byΔX=300×11.7×10−6×5=0.02925 mmmeaning a color misregistration of around 30 μm, which is far from negligible in light of current image target values.